Average Error: 0.5 → 0.2
Time: 12.4s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{100}{x + y} \cdot x\]
\frac{x \cdot 100}{x + y}
↓
\frac{100}{x + y} \cdot x
double f(double x, double y) {
        double r38238147 = x;
        double r38238148 = 100.0;
        double r38238149 = r38238147 * r38238148;
        double r38238150 = y;
        double r38238151 = r38238147 + r38238150;
        double r38238152 = r38238149 / r38238151;
        return r38238152;
}
↓
double f(double x, double y) {
        double r38238153 = 100.0;
        double r38238154 = x;
        double r38238155 = y;
        double r38238156 = r38238154 + r38238155;
        double r38238157 = r38238153 / r38238156;
        double r38238158 = r38238157 * r38238154;
        return r38238158;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.5
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.5

    \[\frac{x \cdot 100}{x + y}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.5

    \[\leadsto \frac{x \cdot 100}{\color{blue}{1 \cdot \left(x + y\right)}}\]

  4. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{100}{x + y}}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{x} \cdot \frac{100}{x + y}\]

  6. Final simplification0.2

    \[\leadsto \frac{100}{x + y} \cdot x\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))